Can we cover the D-surface with straight-strip weaving?

Can we cover the D-surface with straight woven strips? This is a practical question rather than a mathematical one. Strips are developable surfaces (they lie flat on the plane without stretching) so they cannot in truth conform to any area on the D-surface. Also, even flat weaving never actually conforms to the plane nor completely covers it in a water-tight sense, but we can nonetheless weave quite dense fabrics—Skew TeePee falls far short on that measure. The pictures show Skew TeePee dressed up with twists of triangle-pleated paper with encouraging results. The aspect ratio of inter-crossing distance (aka, quarter twist-wavelength) to strip width before dressing was about 4.2, afterwards 1.7. Looks like we would need to get to 1.0 or better to see fabric densities comparable to tabby-weave baskets.